Influence of physical and geometrical uncertainties in the parametric instability load of an axially excited cylindrical shell
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2015
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This work investigates the influence of Young’s modulus, shells thickness, and geometrical imperfection uncertainties on the
parametric instability loads of simply supported axially excited cylindrical shells.TheDonnell nonlinear shallowshell theory is used
for the displacement field of the cylindrical shell and the parameters under investigation are considered as uncertain parameters with
a known probability density function in the equilibrium equation.The uncertainties are discretized as Hermite-Chaos polynomials
together with theGalerkin stochastic procedure that discretizes the stochastic equation in a set of deterministic equations ofmotion.
Then, a general expression for the transversal displacement is obtained by a perturbation procedure which identifies all nonlinear
modes that couple with the linear modes. So, a particular solution is selected which ensures the convergence of the response up to
very large deflections. Applying the standard Galerkin method, a discrete system in time domain that considers the uncertainties
is obtained and solved by fourth-order Runge-Kutta method. Several numerical strategies are used to study the nonlinear behavior
of the shell considering the uncertainties in the parameters. Special attention is given to the influence of the uncertainties on the
parametric instability and time response, showing that the Hermite-Chaos polynomial is a good numerical tool.
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SILVA, Frederico Martins Alves da; Brazao, Augusta Finotti; GONCALVES, Paulo Batista. Influence of physical and geometrical uncertainties in the parametric instability load of an axially excited cylindrical shell. Mathematical Problems in Engineering, London, v. 2015, p. 1-18, 2015.